According to the nonlinear theory, the experiments have been conducted on sample ECG (electrocardiogram) signals of healthy human beings, coronary heart disease patients and adult canines. On the basis of the analyses...According to the nonlinear theory, the experiments have been conducted on sample ECG (electrocardiogram) signals of healthy human beings, coronary heart disease patients and adult canines. On the basis of the analyses of the power spectra, the computation of the correlation dimension and the Lyapunov exponent to a large number of ECG signals, the following conclusions are shown: through the comparative research, (1) the analyses of the power spectra, the computation of the correlation dimension and the Lyapunov exponent to the ECG signals reflect the whole dynamic characteristics of the hearts, and they may become a new method of researching ECG quantitatively to an early diagnose of heart disease. (2) Under normal physiological conditions the cardiac activities are chaotic, while under pathologic conditions the cardiac activities approach regularity. (3) On the basis of the comparative research of human beings and canines, it is revealed that chaos may be a quantitative index to measure the evolution展开更多
Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
Based on the Lü system, a new chaotic system is constructed, which can generate a Lorenz-like attractor, Chen-like attractor, Lii-like attractor and new attractor when its parameters are chosen appropriately. The...Based on the Lü system, a new chaotic system is constructed, which can generate a Lorenz-like attractor, Chen-like attractor, Lii-like attractor and new attractor when its parameters are chosen appropriately. The detailed dynamical behaviours of this system are also investigated, including equilibria and stability, bifurcations, and Lyapunov exponent spectrum. Moreover, a novel analogue circuit diagram is designed for the verification of various attractors.展开更多
Guizhou Province is an important karst area in the world and a fragile ecological area in China. Ecological risk assessment is very necessary to be conducted in this region. This study investigates different character...Guizhou Province is an important karst area in the world and a fragile ecological area in China. Ecological risk assessment is very necessary to be conducted in this region. This study investigates different characteristics of the spatial-temporal changes of vegetation cover in Guizhou Province of Southern China using the data set of SPOT VEGETATION(1999–2015) at spatial resolution of 1-km and temporal resolution of 10-day. The coefficient of variation, the Theil-Sen median trend analysis, and the Mann-Kendall test are used to investigate the spatial-temporal change of vegetation cover and its future trend. Results show that: 1) the spatial distribution pattern of vegetation cover in Guizhou Plateau is high in the east whereas low in the west. The average annual normalized difference vegetation index(NDVI) from west to east is higher than that from south to north. 2) Average annual NDVI improved obviously in the past 17 years. The growth rate of average annual NDVI is 0.028/10 yr, which is slower than that of vegetation in the country(0.048/10 yr) from 1998 to 2007. Average annual NDVI in karst area is lower than that in non-karst area. However, the growing rate of average annual NDVI in karst area(0.030/10 yr) is faster than that in non-karst area(0.023/10 yr), indicating that vegetation coverage increases more rapidly in karst area. 3) Vegetation coverage in the study area is stable overall, but fluctuates in the local scales. 4) Vegetation coverage presents a continuous increasing trend. The Hurst exponent of NDVI in different vegetation types has an obvious threshold in various elevations. 5) The proportion of vegetation cover with sustainable increase is higher than that of vegetation cover with sustainable decrease. The improvement in vegetation cover may expand to most parts of the study area.展开更多
Because atmosphere itself is a nonlinear system and there exist some problems using the linearized equations to study the initial error growth, in this paper we try to use the error nonlinear growth theory to discuss ...Because atmosphere itself is a nonlinear system and there exist some problems using the linearized equations to study the initial error growth, in this paper we try to use the error nonlinear growth theory to discuss its evolution, based on which we first put forward a new concept: nonlinear local Lyapunov exponent. It is quite different from the classic Lyapunov exponent because it may characterize the finite time error local average growth and its value depends on the initial condition, initial error, variables, evolution time, temporal and spatial scales. Based on its definition and the at-mospheric features, we provide a reasonable algorithm to the exponent for the experimental data, obtain the atmospheric initial error growth in finite time and gain the maximal prediction time. Lastly, taking 500 hPa height field as example, we discuss the application of the nonlinear local Lyapunov exponent in the study of atmospheric predictability and get some reliable results: atmospheric predictability has a distinct spatial structure. Overall, predictability shows a zonal distribution. Prediction time achieves the maximum over tropics, the second near the regions of Antarctic, it is also longer next to the Arctic and in subtropics and the mid-latitude the predictability is lowest. Particularly speaking, the average prediction time near the equation is 12 days and the maximum is located in the tropical Indian, Indonesia and the neighborhood, tropical eastern Pacific Ocean, on these regions the prediction time is about two weeks. Antarctic has a higher predictability than the neighboring latitudes and the prediction time is about 9 days. This feature is more obvious on Southern Hemispheric summer. In Arctic, the predictability is also higher than the one over mid-high latitudes but it is not pronounced as in Antarctic. Mid-high latitude of both Hemispheres (30°S―60°S, 30°―60°N) have the lowest predictability and the mean prediction time is just 3―4 d. In addition, predictability varies with the seasons. Most re展开更多
In this paper, the author considers equations with critical exponent in n ≥4 space tions on the initial data, it is proved that there small the initial data are. the Cauchy problem for semilinear wave dimensions. Und...In this paper, the author considers equations with critical exponent in n ≥4 space tions on the initial data, it is proved that there small the initial data are. the Cauchy problem for semilinear wave dimensions. Under some positivity condican be no global solutions no matter how展开更多
We prove the existence of global attractors in H0^1 （Ω） for a nonclassical diffusion equation. Two types of nonlinearity f are considered： one is the critical exponent, and the other is the polynomial growth of ar...We prove the existence of global attractors in H0^1 （Ω） for a nonclassical diffusion equation. Two types of nonlinearity f are considered： one is the critical exponent, and the other is the polynomial growth of arbitrary order.展开更多
A method of the fuzzy cross-correlation factor exponent in dynamics is researched and proposed to diagnose abnormality of cracks in the concrete dam. Moreover, the Logistic time series changing from period-doubling bi...A method of the fuzzy cross-correlation factor exponent in dynamics is researched and proposed to diagnose abnormality of cracks in the concrete dam. Moreover, the Logistic time series changing from period-doubling bifurcation to chaos is tested first using this method. Results indicate that it can distinguish inherent dynamics of time series and can detect mutations. Considering that cracks in the concrete dam constitute an open, dissipative and complex nonlinear dynamical system, a typical crack on the downstream face of a concrete gravity arch dam is analyzed with the proposed method. Two distinct mutations are discovered to indicate that the abnormality diagnosis of cracks in the concrete dam is achieved dynamically through this method. Furthermore, because it can be directly utilized in the measured crack opening displacement series to complete abnormality diagnosis, it has a good prospect for practical applications.展开更多
This study analyzed the spatial and temporal variations in the Normalized Difference Vegetation Index(NDVI) on the Mongolian Plateau from 1982–2013 using Global Inventory Modeling and Mapping Studies(GIMMS) NDVI3 g d...This study analyzed the spatial and temporal variations in the Normalized Difference Vegetation Index(NDVI) on the Mongolian Plateau from 1982–2013 using Global Inventory Modeling and Mapping Studies(GIMMS) NDVI3 g data and explored the effects of climate factors and human activities on vegetation. The results indicate that NDVI has slight upward trend in the Mongolian Plateau over the last 32 years. The area in which NDVI increased was much larger than that in which it decreased. Increased NDVI was primarily distributed in the southern part of the plateau, especially in the agro-pastoral ecotone of Inner Mongolia. Improvement in the vegetative cover is predicted for a larger area compared to that in which degradation is predicted based on Hurst exponent analysis. The NDVI-indicated vegetation growth in the Mongolian Plateau is a combined result of climate variations and human activities. Specifically, the precipitation has been the dominant factor and the recent human effort in protecting the ecological environments has left readily detectable imprints in the NDVI data series.展开更多
We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear Choquard equation -Δu=(integral ((|u(y)|^(2*)_μ/|x-y|~μ)dy) from Ω )|μ|^(2*_μ-2_u)+λu in Ω where Ω is a bounded dota...We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear Choquard equation -Δu=(integral ((|u(y)|^(2*)_μ/|x-y|~μ)dy) from Ω )|μ|^(2*_μ-2_u)+λu in Ω where Ω is a bounded dotain of R^N with Lipschitz boundary, λ is a real parameter, N≥3,2_μ~*=(2 N-μ)/(N-2)is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality.展开更多
The effect of autapse on adjusting the membrane of potentials of neuron is described by imposing a time-delayed feedback on the membrane of neuron in a close loop type,and the Hindmarsh-Rose(HR)neuron under autapse is...The effect of autapse on adjusting the membrane of potentials of neuron is described by imposing a time-delayed feedback on the membrane of neuron in a close loop type,and the Hindmarsh-Rose(HR)neuron under autapse is investigated.Firstly,the electric activity of single HR neuron under electric autapse and chemical autapse is investigated.It is found that quiescent neuron is activated due to appropriate time delay and feedback gain in the autapse,and the autapse plays an important role in waking up neuron.The parameter region for periodic,chaotic activity of neuron under autapse is calculated in a numerical way,and transition from spiking to bursting is observed by increasing the feedback gain and time delay carefully.Furthermore,the collective electric activities of neurons in a ring network is investigated and abundant electric activities are observed due to the competition between the autapse and the time-delayed coupling between adjacent neurons in the network,and time delay in coupling between neurons also plays an important role in enhancing synchronization in the network.展开更多
Extreme climate events play an important role in studies of long-term climate change. As the Earth’s Third Pole, the Tibetan Plateau(TP) is sensitive to climate change and variation. In this study on the TP, the spat...Extreme climate events play an important role in studies of long-term climate change. As the Earth’s Third Pole, the Tibetan Plateau(TP) is sensitive to climate change and variation. In this study on the TP, the spatiotemporal changes in climate extreme indices(CEIs) are analyzed based on daily maximum and minimum surface air temperatures and precipitation at 98 meteorological stations, most with elevations of at least 4000 m above sea level, during 1960–2012. Fifteen temperature extreme indices(TEIs) and eight precipitation extreme indices(PEIs) were calculated. Then, their long-term change patterns, from spatial and temporal perspectives, were determined at regional, eco-regional and station levels. The entire TP region exhibits a significant warming trend, as reflected by the TEIs. The regional cold days and nights show decreasing trends at rates of-8.9 d(10 yr)-1(days per decade) and-17.3 d(10 yr)-1, respectively. The corresponding warm days and nights have increased by 7.6 d(10 yr)-1 and 12.5 d(10 yr)-1, respectively. At the station level, the majority of stations indicate statistically significant trends for all TEIs, but they show spatial heterogeneity. The eco-regional TEIs show patterns that are consistent with the entire TP. The growing season has become longer at a rate of 5.3 d(10 yr)^-1. The abrupt change points for CEIs were examined, and they were mainly distributed during the 1980 s and 1990 s. The PEIs on the TP exhibit clear fluctuations and increasing trends with small magnitudes. The annual total precipitation has increased by 2.8 mm(10 yr)^-1(not statistically significant). Most of the CEIs will maintain a persistent trend, as indicated by their Hurst exponents. The developing trends of the CEIs do not show a corresponding change with increasing altitude. In general, the warming trends demonstrate an asymmetric pattern reflected by the rapid increase in the warming trends of the cold TEIs, which are of greater magnitudes than those of the warm TEIs. This finding indicates a positive shift展开更多
基金This work was supported by the National Natural Science Foundation of China (Grant No. 69974008)the Chinese Postdoctoral Science Foundation and the Natural Science Foundation of Liaoning Province (Grant No. 972194).
文摘According to the nonlinear theory, the experiments have been conducted on sample ECG (electrocardiogram) signals of healthy human beings, coronary heart disease patients and adult canines. On the basis of the analyses of the power spectra, the computation of the correlation dimension and the Lyapunov exponent to a large number of ECG signals, the following conclusions are shown: through the comparative research, (1) the analyses of the power spectra, the computation of the correlation dimension and the Lyapunov exponent to the ECG signals reflect the whole dynamic characteristics of the hearts, and they may become a new method of researching ECG quantitatively to an early diagnose of heart disease. (2) Under normal physiological conditions the cardiac activities are chaotic, while under pathologic conditions the cardiac activities approach regularity. (3) On the basis of the comparative research of human beings and canines, it is revealed that chaos may be a quantitative index to measure the evolution
基金supported by the Scientific Research Fund of Hunan Provincial Education Department (09A058)
文摘Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.
基金Project supported by the National Natural Science Foundation of China （Grant No 60372004）, the Natural Science Foundation of Zhejiang Province, China （Grant No Y105175） and the Science investigation Foundation of Hangzhou Dianzi University, China （Grant No KYS051505010）.
文摘Based on the Lü system, a new chaotic system is constructed, which can generate a Lorenz-like attractor, Chen-like attractor, Lii-like attractor and new attractor when its parameters are chosen appropriately. The detailed dynamical behaviours of this system are also investigated, including equilibria and stability, bifurcations, and Lyapunov exponent spectrum. Moreover, a novel analogue circuit diagram is designed for the verification of various attractors.
基金Under the auspices of National Key Research Program of China(No.2016YFC0502300,2016YFC0502102,2014BAB03B00)National Key Research and Development Program(No.2014BAB03B02)+3 种基金Agricultural Science and Technology Key Project of Guizhou Province of China(No.2014-3039)Science and Technology Plan Projects of Guiyang Municipal Bureau of Science and Technology of China(No.2012-205)Science and Technology Plan of Guizhou Province of China(No.2012-6015)Guangxi Natural Science Foundation of China(No.2014GXNSFBA118221)
文摘Guizhou Province is an important karst area in the world and a fragile ecological area in China. Ecological risk assessment is very necessary to be conducted in this region. This study investigates different characteristics of the spatial-temporal changes of vegetation cover in Guizhou Province of Southern China using the data set of SPOT VEGETATION(1999–2015) at spatial resolution of 1-km and temporal resolution of 10-day. The coefficient of variation, the Theil-Sen median trend analysis, and the Mann-Kendall test are used to investigate the spatial-temporal change of vegetation cover and its future trend. Results show that: 1) the spatial distribution pattern of vegetation cover in Guizhou Plateau is high in the east whereas low in the west. The average annual normalized difference vegetation index(NDVI) from west to east is higher than that from south to north. 2) Average annual NDVI improved obviously in the past 17 years. The growth rate of average annual NDVI is 0.028/10 yr, which is slower than that of vegetation in the country(0.048/10 yr) from 1998 to 2007. Average annual NDVI in karst area is lower than that in non-karst area. However, the growing rate of average annual NDVI in karst area(0.030/10 yr) is faster than that in non-karst area(0.023/10 yr), indicating that vegetation coverage increases more rapidly in karst area. 3) Vegetation coverage in the study area is stable overall, but fluctuates in the local scales. 4) Vegetation coverage presents a continuous increasing trend. The Hurst exponent of NDVI in different vegetation types has an obvious threshold in various elevations. 5) The proportion of vegetation cover with sustainable increase is higher than that of vegetation cover with sustainable decrease. The improvement in vegetation cover may expand to most parts of the study area.
基金This work was supported by the National Natural Science Foundation of China (Grant Nos. 40325015 and 40221503).
文摘Because atmosphere itself is a nonlinear system and there exist some problems using the linearized equations to study the initial error growth, in this paper we try to use the error nonlinear growth theory to discuss its evolution, based on which we first put forward a new concept: nonlinear local Lyapunov exponent. It is quite different from the classic Lyapunov exponent because it may characterize the finite time error local average growth and its value depends on the initial condition, initial error, variables, evolution time, temporal and spatial scales. Based on its definition and the at-mospheric features, we provide a reasonable algorithm to the exponent for the experimental data, obtain the atmospheric initial error growth in finite time and gain the maximal prediction time. Lastly, taking 500 hPa height field as example, we discuss the application of the nonlinear local Lyapunov exponent in the study of atmospheric predictability and get some reliable results: atmospheric predictability has a distinct spatial structure. Overall, predictability shows a zonal distribution. Prediction time achieves the maximum over tropics, the second near the regions of Antarctic, it is also longer next to the Arctic and in subtropics and the mid-latitude the predictability is lowest. Particularly speaking, the average prediction time near the equation is 12 days and the maximum is located in the tropical Indian, Indonesia and the neighborhood, tropical eastern Pacific Ocean, on these regions the prediction time is about two weeks. Antarctic has a higher predictability than the neighboring latitudes and the prediction time is about 9 days. This feature is more obvious on Southern Hemispheric summer. In Arctic, the predictability is also higher than the one over mid-high latitudes but it is not pronounced as in Antarctic. Mid-high latitude of both Hemispheres (30°S―60°S, 30°―60°N) have the lowest predictability and the mean prediction time is just 3―4 d. In addition, predictability varies with the seasons. Most re
基金Project supported by the National Natural Science Foundation of China (No. 10225102)the 973 Project of the Ministry of Science and Technology of China.
文摘In this paper, the author considers equations with critical exponent in n ≥4 space tions on the initial data, it is proved that there small the initial data are. the Cauchy problem for semilinear wave dimensions. Under some positivity condican be no global solutions no matter how
基金Supported in part by the NSFC,Grant(10471056)Trans-Century Training Programme Foundation for the Talents of the State Education Commission
文摘We prove the existence of global attractors in H0^1 （Ω） for a nonclassical diffusion equation. Two types of nonlinearity f are considered： one is the critical exponent, and the other is the polynomial growth of arbitrary order.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51079046, 50909041, 50809025, 50879024)the National Science and Technology Support Plan (Grant Nos. 2008BAB29B03, 2008BAB29B06)+7 种基金the Special Fund of State Key Laboratory of China (Grant Nos. 2009586012, 2010585212)the Fundamental Research Funds for the Central Universities (Grant Nos. 2009B08514, 2010B20414, 2010B14114)China Hydropower Engineering Consulting Group Co. Science and Technology Support Project (Grant No. CHC-KJ-2007-02)Jiangsu Province "333 High-Level Personnel Training Project" (Grant No. 2017-B08037)the Natural Science Foundation of Hohai University (Grant No. 2008426811)Graduate Innovation Program of Universities in Jiangsu Province (Grant No. CX09B_163Z)the Science Foundation for The Excellent Youth Scholars of Ministry of Education of China (Grant No. 20070294023)Dominant Discipline Construction Program Funded Projects of Universities in Jiangsu Province
文摘A method of the fuzzy cross-correlation factor exponent in dynamics is researched and proposed to diagnose abnormality of cracks in the concrete dam. Moreover, the Logistic time series changing from period-doubling bifurcation to chaos is tested first using this method. Results indicate that it can distinguish inherent dynamics of time series and can detect mutations. Considering that cracks in the concrete dam constitute an open, dissipative and complex nonlinear dynamical system, a typical crack on the downstream face of a concrete gravity arch dam is analyzed with the proposed method. Two distinct mutations are discovered to indicate that the abnormality diagnosis of cracks in the concrete dam is achieved dynamically through this method. Furthermore, because it can be directly utilized in the measured crack opening displacement series to complete abnormality diagnosis, it has a good prospect for practical applications.
基金National Key Technology R&D Program of China,No.2013BAK05B01,No.2013BAK05B02National Natural Science Foundation of China,No.41571491,No.61631011Program of Introducing Talents of Discipline to Universities,No.B16011
文摘This study analyzed the spatial and temporal variations in the Normalized Difference Vegetation Index(NDVI) on the Mongolian Plateau from 1982–2013 using Global Inventory Modeling and Mapping Studies(GIMMS) NDVI3 g data and explored the effects of climate factors and human activities on vegetation. The results indicate that NDVI has slight upward trend in the Mongolian Plateau over the last 32 years. The area in which NDVI increased was much larger than that in which it decreased. Increased NDVI was primarily distributed in the southern part of the plateau, especially in the agro-pastoral ecotone of Inner Mongolia. Improvement in the vegetative cover is predicted for a larger area compared to that in which degradation is predicted based on Hurst exponent analysis. The NDVI-indicated vegetation growth in the Mongolian Plateau is a combined result of climate variations and human activities. Specifically, the precipitation has been the dominant factor and the recent human effort in protecting the ecological environments has left readily detectable imprints in the NDVI data series.
基金supported by National Natural Science Foundation of China(Grant Nos.11571317 and 11671364)Natural Science Foundation of Zhejiang(Grant No.LY15A010010)
文摘We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear Choquard equation -Δu=(integral ((|u(y)|^(2*)_μ/|x-y|~μ)dy) from Ω )|μ|^(2*_μ-2_u)+λu in Ω where Ω is a bounded dotain of R^N with Lipschitz boundary, λ is a real parameter, N≥3,2_μ~*=(2 N-μ)/(N-2)is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality.
基金supported by the National Natural Science Foundation of China(Grant Nos.112650081137212211072099 and 11365014)
文摘The effect of autapse on adjusting the membrane of potentials of neuron is described by imposing a time-delayed feedback on the membrane of neuron in a close loop type,and the Hindmarsh-Rose(HR)neuron under autapse is investigated.Firstly,the electric activity of single HR neuron under electric autapse and chemical autapse is investigated.It is found that quiescent neuron is activated due to appropriate time delay and feedback gain in the autapse,and the autapse plays an important role in waking up neuron.The parameter region for periodic,chaotic activity of neuron under autapse is calculated in a numerical way,and transition from spiking to bursting is observed by increasing the feedback gain and time delay carefully.Furthermore,the collective electric activities of neurons in a ring network is investigated and abundant electric activities are observed due to the competition between the autapse and the time-delayed coupling between adjacent neurons in the network,and time delay in coupling between neurons also plays an important role in enhancing synchronization in the network.
基金National Natural Science Foundation of China(41601478,41571391)National Key Research and Development Program of China(2018YFB0505301,2016YFC0500103)
文摘Extreme climate events play an important role in studies of long-term climate change. As the Earth’s Third Pole, the Tibetan Plateau(TP) is sensitive to climate change and variation. In this study on the TP, the spatiotemporal changes in climate extreme indices(CEIs) are analyzed based on daily maximum and minimum surface air temperatures and precipitation at 98 meteorological stations, most with elevations of at least 4000 m above sea level, during 1960–2012. Fifteen temperature extreme indices(TEIs) and eight precipitation extreme indices(PEIs) were calculated. Then, their long-term change patterns, from spatial and temporal perspectives, were determined at regional, eco-regional and station levels. The entire TP region exhibits a significant warming trend, as reflected by the TEIs. The regional cold days and nights show decreasing trends at rates of-8.9 d(10 yr)-1(days per decade) and-17.3 d(10 yr)-1, respectively. The corresponding warm days and nights have increased by 7.6 d(10 yr)-1 and 12.5 d(10 yr)-1, respectively. At the station level, the majority of stations indicate statistically significant trends for all TEIs, but they show spatial heterogeneity. The eco-regional TEIs show patterns that are consistent with the entire TP. The growing season has become longer at a rate of 5.3 d(10 yr)^-1. The abrupt change points for CEIs were examined, and they were mainly distributed during the 1980 s and 1990 s. The PEIs on the TP exhibit clear fluctuations and increasing trends with small magnitudes. The annual total precipitation has increased by 2.8 mm(10 yr)^-1(not statistically significant). Most of the CEIs will maintain a persistent trend, as indicated by their Hurst exponents. The developing trends of the CEIs do not show a corresponding change with increasing altitude. In general, the warming trends demonstrate an asymmetric pattern reflected by the rapid increase in the warming trends of the cold TEIs, which are of greater magnitudes than those of the warm TEIs. This finding indicates a positive shift
